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Research Interests: Surface Waves and Wave-Current Interactions

Surface waves are among the first things anyone observing the ocean encounters. For many researchers, they are merely a nuisance, causing large motions that make instruments fail, overwhelm the delicate signals expected from the deeper waters, and (of course) make many researchers sea-sick and less able to think clearly. However, surface waves are still an active area of research in themselves, since they affect the exchanges of momentum (wind stress), moisture and aerosols, and gas-uptake between the surface layer of water (the oceanic mixed layer) and the air.

Surface waves can directly induce currents in a variety of ways. One is that wave "groups," where a few waves in a row are much larger than the surrounding waves, will induce a trapped "long-wave response," where a mean (Eulerian) flow is set up that runs counter to the direction of wave propagation. The orbital motion of the waves also gives rise to a slight net forward "Stokes drift," so the net motion of actual water parcels is a combination of the Eulerian mean and this drift. This "net parcel motion" is called the Lagrangian mean flow, and represent the actual displacement per unit time of the water itself. In the case of the group-forced long-wave response, the wave-forced Eulerian mean roughly cancels the Stokes drift, so the Lagrangian mean (parcel motion) is more nearly zero. For more details, see

The waves groups themselves are also a curiosity: they are very short (of order 1 wavelength), and yet persist for many wave-periods (7 second period waves which last over 100 seconds as they propagate through the measurement area). This is somewhat counter-intuitive, since surface waves are dispersive, with longer waves travelling faster than short ones, so one expects such a "broadband" group (i.e., short in space) to disperse in a few wave periods. However, it turns out these can still be explained in terms of linear dynamics, with the linear deep-water dispersion relation. The trick is that the wave crests within the group are oriented at an angle to the short dimension of the wave group envelope. For more explanation, see

As an aside, another interesting finding is that the waves can be "unwound" to examine high-frequency waves beyond the normal cutoff for the given sample rate (but only provided that we know which direction is downwind, and only for array lines roughly aligned with the wind): see

Another way waves can generate currents is by breaking, and transferring the large momentum they carry to the underlying flow. This can be particularly effective in the nearshore region, where waves break due to shoaling (see "Nearshore Waves and Currents" below).

Waves also break out in the open ocean, and inject bubbles many meters into the water as well as sending spray up into the air. A major outstanding problem in oceanography lies in understanding the interface between the air and sea, and how this is affected by breaking waves. The challenge is to study the minute details of the motion that are relevant to bubble dynamics and gas exchange, without suffering instrument damage from the large breaking waves themselves. For example,
here is a brief description of a recent attempt to probe upward into
the crest of breaking waves using sound.

Surface waves also have a strong indirect influence on the mixed layer, by stimulating or augmenting a form of wind-induced motion known as "Langmuir circulation" (see the next section of my page, below). While this arises as a fairly complex instability problem, there are also more direct wave-current interactions that can be important.

Much of the confusion about the interaction of waves and currents arises from
the conceptual division of the flow into "Eulerian" (fixed location) versus
"Lagrangian" (fluid-following) frameworks. For example, the difference between
the mean velocity at a fixed point versus that of a drifting particle is
the "Stokes' drift," due to the presence of waves. Often the results of
seemingly complex analyses from one viewpoint can be more simply interpreted
from the other. In any event, the relation between (often intrinsically Lagrangian)
dynamic constraints and the measurements (normally Eulerian) must be borne in mind.
An attempt to write this up in an understandable way is found here:

For the sake of WISE attendees, here is a copy of the lecture I gave as a PDF with movies (44 MB big). The movies only work in Acrobat. You have to click on the (first) image to start each movie, and then click outside the movie before you can go to the next slide. Convenient? Be glad if it even works. Adobe(tm).

Langmuir circulation and mixed layer dynamics

Mixing associated with Langmuir circulation (LC, described below) can be important in the long-term evolution of the mixed layer. The strength and depth of these structures influence the sea surface temperature, and are
important to weather and climate as well as to biology and chemistry.

Langmuir circulation is a form of motion in the wind-mixed layer (rougly speaking, the top 100 m or so that "feels" the wind stress pretty directly). When the wind blows, the water in this layer tends to "spiral" downwind, converging along the surface towards downwelling "streaks" (often made visible by floating seaweed, foam, or oils that collect there but are too buoyant to sink). From there the water, which is moving downwind faster than the rest of the surface water, sinks to the base of the mixed layer, then diverges away to the sides, and gradually upwells between the streaks to start the next cycle.

This form of motion is reinforced by an interaction with the waves. First, the downwind current maximum at the downwelling streaks tends to refract the waves, "bending" the wave momentum away from the streak slightly. Since the waves carry momentum, and the total momentum is conserved, something must be accelerated towards the streak to keep the net momentum steady as the waves are refracted away. That something is the water itself: the water at the surface is pushed toward the streaks by the refracting waves, reinforcing the overall spiral pattern described above. As the water flows along the surface toward the convergence or "streak," it is accelerated by the wind, so by the time it gets there it is going faster than the surrounding water, reinforcing the downwind "jet." Mathematically, the initial stage of this instability can be expressed in a form that indicates exponential growth. Later, finite-amplitude motion effects must stabilize the flow pattern (under steady winds). A somewhat eclectic (some would say "quirky") review of the history of Langmuir circulation is given in

A major field experiment called
"SandyDuck"
took place at the USACE's "Field Research Facility", located near Duck, NC,
on the barrier islands off the East Coast of the USA. The focus time ran from
September through November, 1997. Many people and many measurements were
involved. The goal is to understand the dynamics
of flows near shore. These flows are forced by a combination of wave breaking,
winds, and topographic effects. Of particular interest is the occurrence, form,
and dynamics of rip currents. (Here, "rip currents" are loosely defined as
narrow, offshore-directed flows extending some distance seaward from the shore
through the surf zone.)

Observations of nearshore vorticity.
Preliminary analysis of the evolution of vorticity as observed at SandyDuck has
been undertaken. These observations indicate time-scales of frictional decay of
order 10 minutes for the mean-square-vorticity (enstrophy) over a few fairly
well-defines events.

Recent Results

Some recent work has focused on separating the flow into a part that is horizontally non-divergent (but can have vorticity) and irrotationsl (but can be divergent) parts. The technique is based on the FFT, so it's quite fast. It's applied to two examples: in one, a plume of fresher, lighter water sweeps through the area (likely an out-flow from Chesapeake Bay after rain); in the other, a possible "vortex pair" is seen to propagate through the study region. See
Smith (2008), Vorticity and divergence of surface velocities near shore. (pdf 2.6MB)

Surface waves are important in many of today's concerns. For example,
in planning shipping routes, estimating storm damage risks, and
driving coastal erosion. Global models of directional wave spectra are
routinely run to assist in these endeavors; however, a model is only
as good as the information going into it. The better the observations,
the better the results.

Ocean waves can be tricky to measure- the instruments must
survive the storms that make the biggest waves. Most modern
measurements are fairly simple, giving us estimates of the size of the
waves and (perhaps) the mean direction of wave propagation. But to
model waves from several storms at once, it would be better to have
more detailed directional information. Satellite pictures have great
potential in helping with this; however, the "snapshot" pictures of
the waves arising from satellites have a 180-degree ambiguity: they
can show the orientation of wave crests quite accurately, but cannot
tell which direction they are moving. To do that, one needs arrays
that resolve the waves in both space and time- for example, Doppler
sonar beams extending hundreds of meters along the surface, sampling
every second or so.

Here is a complete 3D surface wave spectrum
P(kx,ky,f),
using data from the dual-PADS deployment at SandyDuck (see the
coastal segment above.) With extensive and
contiguous measurements such as these, many of the assumptions going
into the use of the simpler systems can be directly tested. In particular,
there is no assumption here of a dispersion relation- rather, it can be
seen that the surface waves lie on circles at each frequency, consistent
with the theoretical dispersion.

The Technology

Of course, little of this would be possible without the Doppler sonar technology needed to make measurements over large ranges with such precision and resolution. The "Ocean Physics Group" (OPG) here at SIO has a group of world-class engineers and technicians (M. Goldin, M. Bui, A. Madduri, T. Hugens, A. Aja) dedicated to the design, construction, testing, deploying, trouble-shooting, and analyzing data from (whew!) Doppler sonar systems (and any other hare-brained measurement ideas we come up with). They are supported by two PIs, Rob Pinkel (who, frankly, provides most of the support) and myself. We also have several graduate students and undergraduate interns.

Some of the relevant technology was described above, in the "Some earlier findings about LC" section, and some of the considerations about the effective use of these instruments are outlined in these papers:

Recent Development - BiPADS

We are currently developing a bi-static phased-array Doppler sonar system ("Bi-PADS") with the hope of getting a 2-D, 2-component map of vertical and horizontal velocities on a plane extending right up into the crests of shoaling and breaking waves (sponsored by NSF). Initially we'll try for the 2 in-plane components; subsequently we plan to try a combination of radial and cross-plane components, as the next step towards getting all 3 velocity components over the whole 2-D planar area. There are many technological obstacles to be dealt with (aside from the sheer complexity of the system itself) - including the effects of strong advection on the two acoustic paths, and the substantial variations in the speed of sound in the presence of bubbles. Optimizing the match between the images from the distinct acoustic paths will require some level of estimation of the sound speed anomolies - but this too is valuable information, as it related directly to the bubble content of the fluid mixture.

Schematic view:

And a glimpse of data - even & odd pings alternate transmits from either side. The surface is up near 6m, and you can see some "lumps" in the water sloshing (very slowly!) with the waves. It is reassuring that at least some of the spots are in the same place no matter which side the sound comes from. Proper location of intensity features is sensitive to the detailed geometry of deployment. Playback is about 1/2 real time speed:

An easier-on-the-eyes way to view this is to combine the intensities from the two sides into a common intensity, eliminating the "strobe" effect. This playback is about 1.5 times real time speed:

EquatorMix Cruise Report & Movies

In EquatorMix, we deployed a "High resolution Phased Array Dopper Sonar" (HiPADS), a sonar that broadcasts a fan of 200kHz sound in a thin vertical plane, and beam-forms the returns using an array of receivers, resulting in a pie-shaped measurement area covered by about 64 beams, yielding both backscatter intensity (scatterer density) and Doppler shift (radial velocity). Here is a sample time-series of HiPADS data. This is a 1-minute average, sampled every 30s, formed after correcting each “ping” (2 per second) for tilting and vertical motion due to surface waves.

(Left) Backscatter intensity, reflecting the density of scatters. There are more scatterers (fish, squid, plankton) above the core of the undercurrent, so the intensity is greater there. (Right) Radial velocity relative to the ship (from Doppler shift). The water at 100m depth is moving east (right) at the same speed as the ship, so has zero Doppler shift (relative velocity). Above that, the water is moving slower than the ship or even to the west; thus, there is a blue shift for beam angles forward of vertical, and a red shift at angles aft of vertical. Below 100m, the undercurrent moves east faster than the ship, so the reverse is true: the aft angles are blue-shifted while the forward ones are red-shifted. Below about 150m, the Eastward flow slows to less than ship’s speed again, so there is another reversal of the radial velocity pattern. The vertical streaks at -30 and -50 to -60 meters (aft) are the FCTD going down(-50m to -60m) and coming up (-30m). It comes up slightly forward due to advection by the undercurrent.

This material is based upon work supported by the National Science Foundation under Grant Number (NSF OCE 09-61801).
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.